Phase motion in the $Z^-(4430)$ amplitude in $B^0\to\psi^\prime\pi^-K^+$ decay

TL;DR

This paper introduces an experimental method to confirm the resonant nature of states like the $Z^-(4430)$ by analyzing phase variations through interference in Dalitz plots, tested via Monte Carlo simulations.

Contribution

It presents a novel approach to demonstrate resonance behavior through phase variation analysis, complementing traditional Argand diagram methods.

Findings

Method reveals phase oscillations indicative of resonance.

Monte Carlo tests confirm the method's effectiveness.

Potential to elucidate the internal structure of exotic states.

Abstract

In view of the proliferation in the number of new charmonium states, it is really important to have a experimental way to prove that an observed bump is, indeed, a real resonance. To do that, in this paper we present an alternative method to demonstrate the resonant behavior of a state. With this method, the phase variation of a generic complex amplitude can be directly revealed through interference in the Dalitz-plot region where it crosses a well established resonant state, used as a probe. We have tested the method for the $Z^-(4430)$ state by generating Monte Carlo samples for the $B^0\to \psi^\prime \pi^-K^+$ decay channel. We have shown that the proposed method gives a clear oscillation behavior, related to the phase variation associated to a real resonant state, in the case where the $Z^-(4430)$ is considered as a regular resonance with a strong phase variation. We have also discussed the possibility of using the proposed method complementary to the Argand diagram to determine the internal structure of the $Z^-(4430)$ state.